The present application is based on Disclosure Document serial number 474051, filed May 15, 2000, entitled Optical Profilometry for Periodic Gratings with Three or More Materials per Layer by the same inventors. Therefore, it is requested that the above-specified Disclosure Document be retained in the file of the present patent application.
The present invention relates generally to the measurement of periodic surface profiles using optical techniques such as spectroscopic ellipsometry. In particular, the present invention relates to optical profilometry of profile deviations of semiconductor fabrication processes, more particularly, additional-material deviations in a periodic grating.
There is continual pressure on the semiconductor microchip industry to reduce the dimensions of semiconductor devices. Reduction in the size of semiconductor chips has been achieved by continually reducing the dimensions of transistors and other devices implemented on microchip arrays. As the scale of semiconductor devices decreases, control of the complete profile of the features is crucial for effective chip operation. However, limitations in current fabrication technologies make formation of precise structures difficult. For example, completely vertical sidewalls and completely horizontal top and bottom surfaces in device formation are difficult, if not impossible, to achieve. Sloping sidewalls and top and bottom surfaces are common. Additionally, other artifacts such as xe2x80x9cT-toppingxe2x80x9d (the formation of a xe2x80x9cTxe2x80x9d shaped profile) and xe2x80x9cfootingxe2x80x9d (the formation of an inverse xe2x80x9cTxe2x80x9d shaped profile) are common in microchip manufacturing. Metrology of such details about the profile is important in achieving a better understanding of the fabrication technologies. In addition to measuring such features, controlling them is also important in this highly competitive marketplace. There are thus increasing efforts to develop and refine run-to-run and real-time fabrication control schemes that include profile measurements to reduce process variability.
Optical metrology methods require a periodic structure for analysis. Some semiconductor devices, such as memory arrays, are periodic. However, generally a periodic test structure will be fabricated at a convenient location on the chip for optical metrology. Optical metrology of test periodic structures has the potential to provide accurate, high-throughput, non-destructive means of profile metrology using suitably modified existing optical metrology tools and off-line processing tools. Two such optical analysis methods include reflectance metrology and spectroscopic ellipsometry.
In reflectance metrology, an unpolarized or polarized beam of broadband light is directed towards a sample, and the reflected light is collected. The reflectance can either be measured as an absolute value, or relative value when normalized to some reflectance standard. The reflectance signal is then analyzed to determine the thicknesses and/or optical constants of the film or films. There are numerous examples of reflectance metrology. For example, U.S. Pat. No. 5,835,225 given to Thakur et.al. teaches the use of reflectance metrology to monitor the thickness and refractive indices of a film.
The use of ellipsometry for the measurement of the thickness of films is well-known (see, for instance, R. M. A. Azzam and N. M. Bashara, xe2x80x9cEllipsometry and Polarized Lightxe2x80x9d, North Holland, 1987). When ordinary, i.e., non-polarized, white light is sent through a polarizer, it emerges as linearly polarized light with its electric field vector aligned with an axis of the polarizer. Linearly polarized light can be defined by two vectors, i.e., the vectors parallel and perpendicular to the plane of incidence. Ellipsometry is based on the change in polarization that occurs when a beam of polarized light is reflected from a medium. The change in polarization consists of two parts: a phase change and an amplitude change. The change in polarization is different for the portion of the incident radiation with the electric vector oscillating in the plane of incidence, and the portion of the incident radiation with the electric vector oscillating perpendicular to the plane of incidence. Ellipsometry measures the results of these two changes which are conveniently represented by an angle xcex94, which is the change in phase of the reflected beam xcfx81 from the incident beam; and an angle xcexa8, which is defined as the arctangent of the amplitude ratio of the incident and reflected beam, i.e.,       ρ    =                            r          p                          r          s                    =                        tan          ⁢                      (            Ψ            )                          ⁢                  ⅇ                      j            ⁢                          (              Δ              )                                            ,
where rp is the p-component of the reflectance, and rs is the s-component of the reflectance. The angle of incidence and reflection are equal, but opposite in sign, to each other and may be chosen for convenience. Since the reflected beam is fixed in position relative to the incident beam, ellipsometry is an attractive technique for in-situ control of processes which take place in a chamber.
For example, U.S. Pat. No. 5,739,909 by Blayo et. al. teaches a method for using spectroscopic ellipsometry to measure linewidths by directing an incident beam of polarized light at a periodic structure. A diffracted beam is detected and its intensity and polarization are determined at one or more wavelengths. This is then compared with either pre-computed libraries of signals or to experimental data to extract linewidth information. While this is a non-destructive test, it does not provide profile information, but yields only a single number to characterize the quality of the fabrication process of the periodic structure. Another method for characterizing features of a patterned material is disclosed in U.S. Pat. No. 5,607,800 by D. H. Ziger. According to this method, the intensity, but not the phase, of zeroth-order diffraction is monitored for a number of wavelengths, and correlated with features of the patterned material.
In order for these optical methods to be useful for extraction of detailed semiconductor profile information, there must be a way to theoretically generate the diffraction spectrum for a periodic grating. The general problem of electromagnetic diffraction from gratings has been addressed in various ways. One such method, referred to as xe2x80x9crigorous coupled-wave analysisxe2x80x9d (xe2x80x9cRCWAxe2x80x9d) has been proposed by Moharam and Gaylord. (See M. G. Moharam and T. K. Gaylord, xe2x80x9cRigorous Coupled-Wave Analysis of Planar-Grating Diffractionxe2x80x9d, J. Opt. Soc. Am., vol. 71, 811-818, July 1981; M. G. Moharam, E. B. Grann, D. A. Pommet and T. K. Gaylord, xe2x80x9cFormulation for Stable and Efficient Implementation of the Rigorous Coupled-Wave Analysis of Binary Gratingsxe2x80x9d, J. Opt. Soc. Am. A, vol. 12, 1068-1076, May 1995; and M. G. Moharam, D. A. Pommet, E. B. Grann and T. K. Gaylord, xe2x80x9cStable Implementation of the Rigorous Coupled-Wave Analysis for Surface-Relief Dielectric Gratings: Enhanced Transmittance Matrix Approachxe2x80x9d, J. Opt. Soc. Am. A, vol. 12, 1077-1086, May 1995.) RCWA is a non-iterative, deterministic technique that uses a state-variable method for determining a numerical solution. Several similar methods have also been proposed in the last decade. (See P. Lalanne and G. M. Morris, xe2x80x9cHighly Improved Convergence of the Coupled-Wave Method for TM Polarizationxe2x80x9d, J. Opt. Soc. Am. A, 779-784, 1996; L. Li and C. Haggans, xe2x80x9cConvergence of the coupled-wave method for metallic lanelar diffraction gratingsxe2x80x9d, J. Opt. Soc. Am. A, 1184-1189, June, 1993; G. Granet and B. Guizal, xe2x80x9cEfficient Implementation of the Coupled-Wave Method for Metallic Lamelar Gratings in TM Polarizationxe2x80x9d, J. Opt. Soc. Am. A, 1019-1023, May, 1996; U.S. Pat. No. 5,164,790 by McNeil, et al; U.S. Pat. No. 5,867,276 by McNeil, et al; U.S. Pat. No. 5,963,329 by Conrad, et al; and U.S. Pat. No. 5,739,909 by Blayo et al.)
Generally, an RCWA computation consists of four steps:
The grating is divided into a number of thin, planar layers, and the section of the ridge within each layer is approximated by a rectangular slab.
Within the grating, Fourier expansions of the electric field, magnetic field, and permittivity leads to a system of differential equations for each layer and each harmonic order.
Boundary conditions are applied for the electric and magnetic fields at the layer boundaries to provide a system of equations.
Solution of the system of equations provides the diffracted reflectivity from the grating for each harmonic order.
The accuracy of the computation and the time required for the computation depend on the number of layers into which the grating is divided and the number of orders used in the Fourier expansion.
The diffracted reflectivity information which results from an RCWA computation can be used to determine the details of the profile of a semiconductor device. Generally, reflectivities for a range of different possible profiles of a given semiconductor device are numerically calculated using RCWA and stored in a database library. Then, the actual diffracted reflectivity of the given device is measured as disclosed, for example, in co-pending U.S. patent application Ser. No. 09/764,780 for Caching of Intra-Layer Calculations for Rapid Rigorous Coupled-Wave Analyses filed Jan. 25, 2000 by the present inventors which is hereby incorporated in its entirety into the present specification, or X. Niu, N. Jakatdar, J. Bao and C. J. Spanos, xe2x80x9cSpecular Spectroscopic Scatterometryxe2x80x9d IEEE Trans. on Semiconductor Manuf., vol. 14, no. 2, May 2001. The reflected phase and magnitude signals obtained, in the case of ellipsometry, and relative reflectance, in the case of reflectometry, are then compared to the library of profile-spectra pairs generated stored in the library. A phase and/or amplitude measurement will be referred to in the present specification as the xe2x80x9cdiffracted reflectivity.xe2x80x9d The matching algorithms that can be used for this purpose range from simple least squares approach, to a neural network approach that associates features of the signal with the profile through a non-linear relationship, to a principal component based regression scheme. Explanations of each of these methods is explained in numerous text books on these topics such as Chapter 14 of xe2x80x9cMathematical Statistics and Data Analysisxe2x80x9d by John Rice, Duxbury Press and Chapter 4 of xe2x80x9cNeural Networks for Pattern Recognitionxe2x80x9d by Christopher Bishop, Oxford University Press. The profile associated with the RCWA-generated diffracted reflectivity that most closely matches the measured diffracted reflectivity is determined to be the profile of the measured semiconductor device.
In semiconductor manufacturing, a number of processes may be used to produce a periodic structure having two materials in the periodic direction. In the present specification the xe2x80x9cnominalxe2x80x9d number of materials occurring in the periodic direction is considered to be the maximum number of materials that lie along any of the lines which pass through the periodic structure in the direction of the periodicity. Accordingly, structures having a nominal two materials in the periodic direction have at least one line along the direction of periodicity passing through two materials, and no lines along the direction of periodicity passing through more than two materials. Additionally, it should be noted that when specifying the nominal number of materials occurring along a periodic direction of a structure in the present specification, the gas, gases or vacuum in gaps between solid materials is considered to be one of the materials. For instance, it is not necessary that both materials occurring in the periodic direction of a nominal two material periodic structure be solids.
An example of a structure 100 with two materials in a layer is shown in the cross-sectional view of FIG. 1A, which shows two periods of length D of a periodic portion of the structure 100. The structure 100 consists of a substrate 105, with a thin film 110 deposited thereon, and a periodic structure on the film 110 which consists of a series of ridges 121 and grooves 122. In exemplary structure 100, each ridge 121 has a lower portion 131, a middle portion 132 and an upper portion 133. It should be noted that according to the terminology of the present invention, the lower, middle and upper portions 131-133 are not xe2x80x98layers.xe2x80x99 In exemplary structure 100 of FIG. 1A, the lower, middle and upper portions 131-133 are each composed of a different material. The direction of periodicity is horizontal on the page of FIG. 1A, and it can be seen that a line parallel to the direction of periodicity may pass through at most two different materials. For instance, a horizontal line passing through the middle portion 132 of one of the ridge structures 121, passes through the middle portion 132 of all of the ridge structures 121, and also passes through the atmospheric material 122. That is, there are two materials in that region. (It should be noted that a line which is vertical on the page of FIG. 1A can pass through more than two materials, such as a line passing through the lower, middle and upper portions 131-133 of a ridge structure, the thin film 110, and the substrate 105, but according to the terminology of the present specification this structure 100 is not considered to have a nominal three or more materials in the periodic direction.)
A close-up cross-sectional view of a ridge structure 121 is shown in FIG. 1B with the structure being sectioned into what are termed xe2x80x98harmonic expansion layersxe2x80x99 or simply xe2x80x98layersxe2x80x99 in the present specification. In particular, the upper portion 133 is sectioned into five harmonic expansion layers 133.1 through 133.5, the middle portion 132 is sectioned into nine harmonic expansion layers 132.1 through 132.9, the lower portion 131 is sectioned into six harmonic expansion layers 131.1 through 131.6, and five harmonic expansion layers 110.1 through 110.5 of the thin film 110 are shown. All layer boundaries are horizontal planes, and it should be understood that harmonic expansion layers 133.1-133.5, 132.1-132.9, 131.1-131.6 and 110.1-110.5 may have differing thicknesses. For clarity of depiction, the harmonic expansion layers 133.1-133.5, 132.1-132.9, 131.1-131.6 and 110.1-110.5 are not shown to extend into the atmospheric material, although they are considered to do so. As can be seen in FIG. 1A, a structure having two materials occurring in a periodic direction will necessarily have two materials in an harmonic expansion layer.
With respect to semiconductors having a periodic structure with a nominal two materials in periodic direction, it is often the case that the widths of the solid structures in the periodic direction is important to proper operation of the device being produced. For example, the width of a structure (such as a transistor gate) can determine how quickly or slowly a device will operate. Similarly, the width of a conductor can determine the resistance of the conductor, or the width of a gap between two conductors can determine the amount of current leakage. Furthermore, the geometry of a structure in the periodic direction can also impact the geometry of successive layers of the chip.
Because the characteristic dimension of a structure in a direction orthogonal to the normal vector of the substrate generally has the most impact on the operation of a device and the fabrication of the characteristic dimension in successive layers of the chip, that dimension is referred to as the xe2x80x9ccriticalxe2x80x9d dimension. Because of the importance of critical dimension, it is common to use both the RCWA techniques discussed above and various other types of microscopy (such as critical-dimension scanning electron microscopy, cross-sectional scanning electron microscopy, atomic force microscopy, and focused ion beam measurement) to measure critical dimensions. While these techniques can generally adequately measure critical dimensions of structures having a single solid material along a line in the periodic direction, none of these techniques can make accurate measurements of critical dimensions of multiple material components of structures when more than a single solid material occurs in the periodic direction. In particular, such techniques generally cannot make accurate measurements of materials having more than two materials in a periodic direction.
However, a process which is intended to produce a structure with only two materials per layer may have deviations which result in more than two materials in a layer. For example, in FIG. 2A a semiconductor device 810 is shown in which troughs 812 have been etched in a vertical portion 814, such as a series of ridges 815. Such a process nominally produces a structure having two materials along each line in the periodic direction: the solid material of the ridges 815 and the atmospheric material in the troughs 812. However, as shown in FIG. 2B, which illustrates a common manufacturing defect on semiconductor device 810, when etching the troughs 812, a thin polymer layer 818 can remain coated on the side and bottom walls of the troughs 812.
Therefore, device 810 has three materials along the line 820 in the periodic direction: the material of ridges 815, the material of polymer 818, and the atmospheric gas in trough 812. And, as noted above, techniques discussed above which can measure critical dimensions of periodic structures having a nominal two materials in the periodic direction cannot be used to accurately measure the dimensions of multiple solid materials within structures having more than two materials in the periodic direction. Specifically, techniques ordinarily used to measure the width of the ridges 815 will not yield an accurate measurement result when polymer 818 is present. This is because such techniques generally cannot distinguish between the material of ridges 815 and the material of polymer 818.
A second example of a structure which is intended to nominally have only two materials in the periodic direction but which, due to additional-material deviations, has more than two materials in the periodic direction can occur in performing chemical mechanical polishing (xe2x80x9cCMPxe2x80x9d), as is shown in FIG. 3A. FIG. 3A shows a semiconductor device 700 having a substrate 710 with a nitride layer 714 formed thereon. Troughs 712 are etched in the substrate 710 and nitride layer 714. Silicon dioxide plugs 716 are then placed in troughs 712. This results in a periodic structure which has either one or two materials in the periodic direction. In particular, the substrate material 710 and the material of the silicon dioxide plugs 716 fall along line 722; the material of nitride layer 714 and the material of the silicon dioxide plugs 716 fall along line 718; and the material of the substrate 710 falls along line 724.
After the silicon dioxide plugs 716 have been formed, such a device 700 would typically be further processed using a technique referred to as xe2x80x9cshallow trench isolation CMPxe2x80x9d. This technique is intended to smooth the top face of the device so that the top of nitride layer 714 and the top of the silicon dioxide plugs 716 both come to the same level, shown by line 720. However, because silicon dioxide is softer than nitride, silicon dioxide plugs 716 will erode further than the nitride layer 714. This results in portions of silicon dioxide plugs 716 dipping below the top surface of the nitride layer, and is known as xe2x80x9cdishingxe2x80x9d of silicon dioxide plugs 716. And, as shown in FIG. 3A along line 718, near the top of the nitride layer 714, device 700 can has three materials occurring in the periodic direction: nitride, silicon dioxide and the atmospheric material in those regions where the dishing has resulted in the top surface 717 of the silicon dioxide plugs 716 being below the level of line 718.
This type of deviation is referred to in the present specification as a xe2x80x9ctransversexe2x80x9d deviation because it is transverse to the periodic direction of the structure and is transverse to what would generally be the direction along which the critical dimension is measured. That is, the deviation occurs in the direction normal to the face of device 700 (in a vertical direction in FIG. 3), rather than along the periodic direction. In contrast, the semiconductor manufacturing industry generally focuses on deviations in the critical dimension, such as T-topping discussed earlier. Accordingly, the idea of measuring the extent of any dishing occurring in a semiconductor manufacturing process has not generally arisen in the semiconductor fabrication industry since transverse deviations have not been considered to have substantial effects on the operation of devices or the fabrication of subsequent layers.
However, it is here predicted that with continuing technological innovations allowing the size of semiconductor devices to steadily shrink, the functioning of semiconductor devices will become increasingly dependent on precise fabrication control and metrology along the transverse direction, and precise fabrication and control of additional-material deviations. Furthermore, recently developed devices have been designed with their critical dimension (i.e., the dimension having the greatest effect on the operation of the device) along the normal to the substrate, i.e., along the direction that the present specification has previously referred to as the transverse direction. Therefore, it is here predicted that future generations of semiconductor systems will both have devices with their critical dimension parallel to the substrate, and devices with their critical dimension perpendicular to the substrate.
A method and system in accordance with the present invention allows measurement of semiconductor fabrication methods which ideally have only two materials along a line in a periodic direction, but which have deviations which result in more than two materials occurring along a line in a periodic direction.
A method for metrology of additional-material structural deviations of a nominal periodic structure by comparison of a measured diffraction spectrum from a target periodic structure with a calculated diffraction spectrum from a hypothetical deviated periodic structure, where the hypothetical deviated periodic structure is defined by applying the additional-material structural deviations to said nominal periodic structure. The hypothetical deviated periodic structure has a direction of periodicity x, a direction of essentially-infinite extension y which is orthogonal to the x direction, and a normal direction z which is orthogonal to both the x and y directions. A plurality of layers are defined parallel to an x-y plane. An x-z plane cross-section of the periodic structure is sectioned into a plurality of stacked rectangular sections such that only two materials from the nominal periodic structure are within each of the plurality of layers and at least three materials are within at least one of the plurality of layers in the hypothetical deviated periodic structure. A harmonic expansion of a function of the permittivity xcex5 is performed along the direction of periodicity x for each of the layers, including the layer or layers in the hypothetical deviated periodic structure which include(s) at least three materials. Fourier space electromagnetic equations are then set up in each of the layers using the harmonic expansion of the function of the permittivity xcex5 for each of the layers and Fourier components of electric and magnetic fields in each layer. The Fourier space electromagnetic equations are then coupled based on boundary conditions between the layers, and solved to provide the calculated diffraction spectrum.
In a second aspect of the present invention, generation of the diffracted reflectivity of a periodic grating to determine values of structural properties of the periodic grating includes dividing the periodic grating into a plurality of hypothetical layers at least one of which is formed across at least first, second and third materials in the periodic grating. Each hypothetical layer has its normal vector orthogonal to the direction of periodicity, and each hypothetical layer has one of a plurality of possible combinations of hypothetical values of properties for that hypothetical layer. Sets of hypothetical layer data are then generated. Each set of hypothetical layer data corresponds to a separate one of the plurality of hypothetical layers. The generated sets of hypothetical layer data are processed to generate the diffracted reflectivity that would occur by reflecting electromagnetic radiation off the periodic grating.
Preferably, each hypothetical layer is subdivided into a plurality of slab regions with each slab region corresponding to a separate material within the hypothetical layer. Also, preferably, generating sets of hypothetical layer data includes expanding the real space permittivity or the real space inverse permittivity of the hypothetical layers in a one-dimensional Fourier transformation along the direction of periodicity of the periodic grating. Preferably, the Fourier transform is formulated as a sum over boundaries between materials in each layer.
In a third aspect of the present invention, a method of generating an expression of the permittivity of a target periodic grating having more than two materials in a periodic direction for use in an optical profilometry formalism for determining a diffracted reflectivity of the target periodic grating includes dividing the target periodic grating into a plurality of hypothetical layers. At least one of the hypothetical layers is formed across each of at least a first, second and third material occurring along a line parallel to a direction of periodicity of the target periodic grating. At least one of the plurality of hypothetical layers is subdivided into a plurality of hypothetical slabs to generate a plurality of hypothetical boundaries. Each of the plurality of hypothetical boundaries corresponds to an intersection of at least one of the plurality of hypothetical layers with one of at least the first, second and third materials. A permittivity function is determined for each of the plurality of hypothetical layers. Then, a one-dimensional Fourier expansion of the permittivity function of each hypothetical layer is completed along the direction of periodicity of the target periodic grating by summing the Fourier components over the plurality of hypothetical boundaries to provide harmonic components of the at least one permittivity function. A permittivity harmonics matrix is then defined including the harmonic components of the Fourier expansion of the permittivity function.
A system of the present invention includes a microprocessor configured to perform the steps of the methods discussed above. Additionally, a computer readable storage medium in accordance with the present invention contains computer executable code for instructing a computer to operate to complete the steps of the methods discussed above.